a r X i v :g r -q c /9611069v 3 17 O c t 2000“No–Hair”Theorem for Spontaneously Broken Abelian Models in Static Black Holes
Eloy Ay′o n–Beato
Departamento de F′?sica,CINVESTAV–IPN,
Apartado Postal 14–740,C.P.07000,M′e xico,D.F.,MEXICO.
The vanishing of the electromagnetic ?eld,for purely electric con?gurations of spontaneously
broken Abelian models,is established in the domain of outer communications of a static asymptot-
ically ?at black hole.The proof is gauge invariant,and is accomplished without any dependence on
the model.In the particular case of the Abelian Higgs model,it is shown that the only solutions
admitted for the scalar ?eld become the vacuum expectation values of the self–interaction.
04.70.Bw,04.70.-s,04.40.-b,04.20.Ex
I.INTRODUCTION The classical and strongest version of the “no–hair”conjecture establishes that a stationary black hole is uniquely described by global charges,i.e.,conserved charges associated with massless gauge ?elds,expressed by surface integrals at the spatial in?nity i o [1].In particular,the conjecture excludes the existence of massive ?elds in the domain of outer communications J ( of a stationary black hole.This fact rests on the idea that in the black hole transition to stationarity “everything that can be radiated away will be radiated away”(cf.[2]),so,the only classical degrees of freedom of a stationary black hole are those corresponding to non–radiative multipole moments;massive ?elds are automatically excluded because all their multipoles are radiative [1].The absence of massive “hair”was shown early in the Bekenstein pioneering works for massive scalar ?elds,Proca–massive spin–1?elds,and massive spin–2?elds [3–5].An alternative demonstration for Proca ?elds can be found in [6].The “no–hair”theorem for massive vector ?elds is a useful tool for excluding the existence of new black hole solutions for very complicated theories as metric–a?ne gravity,where a relevant sector of this theory reduces to an e?ective Einstein–Proca system [7].It is well–known that ?elds acquire mass not only kinematically,as in the previous cases,but also through a dynamical mechanism of spontaneous symmetry breaking.This is the case of spontaneously broken Abelian models describing a charged scalar ?eld with a self–interaction having nonzero vacuum expectation values,and minimally coupled to a massless Abelian gauge ?eld.The “no–hair”conjecture for these models has been previously enunciated as [8]:any stationary black hole solution,such that all gauge–invariant observables are non–singular,must have a vanishing electromagnetic ?eld,in the domain of outer communications J ( of the black hole .The simplest of this systems is the Abelian Higgs model (Mexican–hat self–interaction)for which a “no–hair”theorem was shown in [9],proving the vanishing of the gauge ?eld for spherically symmetric static black holes.This proof has been considered unsatisfactory [10]because it is based on an inconsistent gauge choice.Improved versions have been recently given [11–13],without the original restrictions criticized in [10].The subject of this paper is twofold,?rst,to relax the spherically symmetric assumption in the previously quoted
contributions,by working with general static asymptotically ?at systems,and second,to extent the “no–hair”theo-rem to more general Abelian models than the Higgs model,i.e.,for general spontaneously broken self–interactions.Emphasis is given on asymptotically ?at black holes only,this way we exclude from consideration black holes pierced by a cosmic string [14]—with the corresponding nontrivial behavior of the Abelian ?eld—,as it has been previously pointed by Bekenstein [13,15],these last con?gurations are not asymptotically ?at since they present the angular de?cit inherent to the presence of topological defects.The basic di?erence between these con?gurations is that for the string–pierced black holes the scalar ?eld satisfy boundary conditions at in?nity in accordance with the existence of a topological defect,i.e.,the scalar ?eld is con?ned to the vacuum only in a circle at in?nity,which implies the developing of a cosmic string at the interior of the circle,whereas for asymptotically ?at black holes the scalar ?eld approaches the vacuum in all directions at in?nity.
For a static black hole,the Killing ?eld k coincides with the null generator of the event horizon H +and is timelike
and hypersurface orthogonal in all the domain of outer communications J ( .This allow us to choose,by simply connectedness of J ( [16],a global coordinate system (t,x i ),i =1,2,3,in all J ( [17],such that k =?/?t and the
metric reads
g =?V dt 2+γij dx i dx j ,(1)
where V and γare t –independent,γis positive de?nite in all J ( ,and V is positive in all J ( and vanishes in H +.
From (1)it can be noticed that staticity implies the existence of a time–reversal isometry t →?t .
In the next Sec.II the vanishing of the electromagnetic?eld in the domain of outer communications J( of a static asymptotically?at black hole is demonstrated for purely electric con?gurations of a generic spontaneously broken Abelian model.At the end of Sec.II the conditions for establishing a“no–hair”theorem for purely magnetic con?gurations are also analyzed.Sec.III is devoted to show,in the particular case of the Abelian Higgs model,that the charged scalar?eld is con?ned to its vacuum in J( .Conclusions are given in Sec.IV.
II.“NO–HAIR”THEOREM FOR THE ABELIAN GAUGE FIELD
The action describing the coupling to gravity of the relevant models to be considered is
S=1
κ
R?
1
2κR?
1
2
?αρ?αρ?
1
2
U(ρ),(3)
with Jα≡eρ2(?αθ?eAα).The potential U(ρ)is a non–negative function achieving its minima at nonzero values v a,cf.Fig.1,and it is assumed thatρasymptotically approaches to any one of this values.The Abelian symmetry FIG.1.Example of a spontaneously broken potential with?ve types of non–vanishing vacuum expectation values.The
positive real numberεis such that0<ε≤v1,and it will be used to show thatρis a non–vanishing function at the horizon. of the models is expressed by the invariance of the Lagrangian(3)under the gauge transformationsθ→θ+eΛ, Aα→Aα+?αΛ.From the Lagrangian(3),the Einstein–Maxwell–Scalar equations for the involved?elds are established
1
4πFαμFνα+?μρ?νρ+
1
2
gμν FαβFαβ
2
U′(ρ)+
1
where U ′(ρ)≡dU (ρ)/dρ.
We would like to emphasize that the Reissner–Nordstr¨o m black hole is not a solution of the above equations;the system we are dealing with is an Abelian Higgs model,i.e.,a charged (e =0)scalar ?eld minimally coupled to an Abelian gauge ?eld,and with a self–interaction having nonvanishing vacuum expectation values.The coupling of this system to gravity (4)–(6),does not reduce in no one case to the Einstein–Maxwell system,and therefore,it does not contain the Reissner–Nordstr¨o m black hole as a solution.This becomes apparent from the Lagrangian (2):for constant values of the charged scalar ?eld,Φ=const.,a mass term,e 2|const.|2A μA μ,is present,which converts the Abelian gauge ?eld in a massive Proca–like spin–1?eld,for which there exist no static black hole solutions except the Schwarzschild one,as it was pointed out in the introduction [4,6].For a zero value of the scalar ?eld,the mass term vanishes,but,an e?ective cosmological constant,Λe?=κU (0)/2,arises,this is due to the spontaneously broken behavior of the self–interaction,which requires U (0)=0.In this case,we lost asymptotic ?atness and,consequently,the Reissner–Nordstr¨o m black hole cannot be a solution of the resulting system.Other is the situation when there is no spontaneously symmetry breaking,i.e.,U (0)=0,in this case the model reduces to the Einstein–Maxwell system for vanishing scalar ?eld and the existence of the Reissner–Nordstr¨o m black hole is assured,but this is not the case we will dealt with in the paper.
We shall assume that the gauge ?eld shares the same symmetries of the metric,namely,it is stationary,￡k F =0.Consequently with a (metric–)static con?guration (1),we will also assume the existence of electromagnetic staticity,i.e.,the Maxwell ?eld F αβand the Maxwell equations (5)are invariant under time–reversal transformations.The time–reversal invariance of Maxwell equations (5)requires that,in the coordinates chosen in (1),J t and F ti remain unchanged while J i and F ij change sign,or the opposite scheme,i.e.,J t and F ti change sign as long as J i and F ij remain unchanged under time reversal [4].However,this isometry should not change gauge–invariant observables,therefore J i and F ij must vanish in the ?rst case,while J t and F ti vanish in the second one.Hence,staticity on the metric and material sources implies the existence of two nonoverlapping cases:a purely electric case (I)and a purely magnetic case (II).
Now we are ready to proof the “no–hair”statement for the gauge ?eld,i.e.,for spontaneously broken Abelian
model the electromagnetic ?eld vanishes in the domain of outer communications J ( of a static asymptotically ?at
black hole.Let V ? J ( be the open region bounded by the spacelike hypersurface Σ,the spacelike hypersurface Σ′,and pertinent portions of the horizon H +,and the spatial in?nity i o .The spacelike hypersurface Σ′is obtained
by shifting each point of Σa unit parametric value along the integral curves of the Killing ?eld k .Multiplying the Maxwell equations (5)by J α/ρ2and integrating by parts over V ,after applying the Gauss theorem,and using that J α/ρ2=2e (?αθ?eA α),one obtains
Σ′
? Σ+ H +∩V 12F αβF αβ+4πV vanishes [9,11].For the remaining boundary integral
at the portion of the horizon H +∩ρ2J αF αβd Σβ= J αF αβl β
ρ2(l μl μ) dσ.(8)
In order to demonstrate that the last integrand vanishes it is su?cient to prove that the quantities appearing at the right hand side of (8)are such that:J αF αβl β/ρ2vanishes and J αF αβn β/ρ2remains bounded at the horizon.We shall establish the behavior of these quantities at the horizon by studying some invariants constructed from the curvature.By using Einstein equations (4),we obtain the following two equivalent expressions,
2
2π+ 2J μ?μρ
2π?J μJ μ
2π+?μρ?μρ
2+ U (ρ)+J μJ μ
πe 2ρ2
J μF αμJ νF να+1
=G2
eρ
2
+ F e2ρ2 2+ F e2ρ2 2
+(U(ρ)+?μρ?μρ)2+
1
π
?μρFαμ?νρFνα,(10)
where F≡FαβFαβ/4,G≡?FαβFαβ/4,and?Fαβstands for the Hodge dual(?Fαβ=ημναβFμν/2).It is important to note that the previous Eqs.only di?er in the sign inside the fourth term,and in the fact that the last term is written in each case with?Fαβand Fαβ,respectively.
Since the horizon is a smooth surface,the left hand side of the above Eqs.is bounded on it.For the purely electric case(I),the last two terms in the right hand side of(9)are non–negative,the remaining terms are perfect square,and consequently each term in the right hand side of(9)is bounded at the horizon.In particular,the bounded behavior of the sixth term involving the quantities U(ρ)and?μρ?μρimplies,from the non–negativeness of these quantities,that they are also bounded at the horizon.It follows from the bounded behavior of the perfect–square terms where U(ρ) and?μρ?μρare combined with the quantities JμJμ/e2ρ2and F,respectively,that the last mentioned quantities are also bounded at the horizon.Thus,any quantity appearing in the right hand side of(9)is bounded at the horizon, in particular U(ρ),F and JμJμ/ρ2.The same conclusions can be achieved,along the same lines of reasoning,for the purely magnetic case(II),but this time using the right hand side of Eq.(10).Other invariants can be built from the Ricci curvature(4)by means of l and n,which are well–de?ned smooth vector?elds on the horizon.The?rst invariant reads
1
4πIμIμ+(nμ?μρ)2+
1
2 F
κRμνlμlν=
1
e2ρ2
(Jμlμ)2?
lμlμ
2π
?U(ρ) ,(12)
where Eμ≡Fμνlνis the electric?eld at the horizon.Once again the bounded behavior of the invariant F and the potential U(ρ)can be used to achieve the vanishing of the last term of(12).Since E is orthogonal to the null generator l,it must be spacelike or null(EμEμ≥0),consequently each term on the right hand side of(12)vanishes independently,which implies that Jμlμ/ρ=0and that E is proportional to the null generator l at the horizon, i.e.,E=?(Eαnα)l.The vanishing of lμ?μρ,only reproduces the fact that l coincides with the Killing?eld at the horizon.The last invariant to be studied gives the following relation:
1
4π+
U(ρ)
4π
(Eμnμ)2+(lμ?μρ)(nν?νρ)+ Jμlμeρ ,(13)
where it has been used that E=?(Eαnα)l.Because nν?νρand Jνnν/ρare bounded at the horizon,and Jμlμ/ρ= 0=lμ?μρ,the last two terms in the right hand side of(13)vanish,thus Eμnμis bounded at the horizon as consequence of the bounded behavior of the left hand side of(13).
Summarizing,the study of the quoted invariants at the horizon leads to the following conclusions:Eμnμ,Jμnμ/ρ, nμ?μρ,JμJμ/ρ2,and IμIμare bounded at the horizon,while Jμlμ/ρ=0and E=?(Eαnα)l in the same region. Now we are in position to make a more detailed analysis of the su?cient conditions for the vanishing of the integrand (8)over the horizon,i.e.,JαFαβlβ/ρ2vanishes and JαFαβnβ/ρ2remains bounded at the https://www.doczj.com/doc/db12044384.html,ing the de?nition Eμ≡Fμνlνand that E=?(Eαnα)l,we obtain for the?rst quantity at the horizon
JαFαβlβ
ρ(Eμnμ)
Jνlν
constructed with l,n,and a pair of linearly independent spacelike vectors,these last ones being tangent to the spacelike cross sections of the horizon,the J and I vectors can be written as
J=?(Jαnα)l+J⊥,(15)
I=?(Iαlα)n+I⊥,(16) where J⊥and I⊥are the projections,orthogonal to l and n,on the spacelike cross sections of the https://www.doczj.com/doc/db12044384.html,ing(15) and(16)it is clear that JμJμ=J⊥μJ⊥μ,and IμIμ=I⊥μI⊥μ,i.e.,the contribution to these bounded magnitudes comes only from the spacelike sector orthogonal to l and n.With the help of(15)and(16)the other quantity appearing in the integrand(8)can be written as
JαFαβnβ
ρ2=
1
ρ
+
J⊥αI⊥α
2fε(ρ)U′(ρ)+
fε(ρ)
V vanishes,becauseρtakes asymptotically some of the values v a minimizing the potential function U(ρ),
-0.4
-0.2
0.2
0.4
FIG.2.The graph of the auxiliar function f ε(t ).
then by
(19)
the
integrand vanishes
there.The
same
happens
to
the
integral over
H
+
∩
2f ε(ρ)U ′(ρ)?V f ε(ρ)
ρ2(J t )2 dv =0.(23)
The nonpositiveness of the above integrand,which is minus the sum of squared terms,implies that the integral is
vanishing only if F ti and J t vanish everywhere in V ,and hence in all of J ( .
Finally,we would like to explain why our proof on the nonvanishing ofρfails in the purely magnetic case(II). This is due to the fact that the last term in the volume integral(22)must be replaced,in the purely magnetic case (II),by the non–positive quantity fε(ρ)γij J i J j/4eρ3(cf.Fig.2),since the?rst two terms are again non–negative the integrand have no de?nite sign and it is impossible to deduce the vanishing of it from the vanishing of the integral.So, the nonvanishing ofρfor the purely magnetic case(II)must be justi?ed using a di?erent approach.We are looking for a shortcut to solve this impasse,since we believe that the“no–hair”conjecture applies also to this case.For any successful justi?cation of the conditionρ|H+=0,the rest of the proof follows in this way:the nonvanishing ofρimplies again the vanishing of the integrand(8)over the horizon,having no contribution from boundary integrals in (7),the volume integral for the purely magnetic case(II)can be written,using the coordinates from(1),as
e2ρ2γij J i J j dv=0,(24)
V
where again the non–negativeness of the integrand implies that the vanishing of the integral is satis?ed only if F ik and J i vanish everywhere in V,and hence in all of J( .
III.“NO–HAIR”THEOREM FOR THE SCALAR FIELD IN THE ABELIAN HIGGS MODEL
It is reasonable to expect,from the“no–hair”conjecture,that the only possible solutions for a scalar model in the domain of outer communications J( of a stationary asymptotically?at black hole become the vacuum expectation values of the self–interaction.In the models considered in this paper this implies the uniqueness of the scalar states Φa=v a exp iθ,where v a=0are the values minimizing the potential function U(ρ).We now concentrate our attention in the Abelian Higgs model,for which U(ρ)has a single minimum at v,and we shall show the truthfulness of the last statement for the purely electric case(I),without any dependence on the speci?c choice of the potential.The result is obtained by applying the same procedure used above for the Eq.(6),with the function fε(ρ)replaced this time by the function tanh(ρ?v),and taking into account that Jμ=0,arriving now at
(sech2(ρ?v)γij?iρ?jρ+tanh(ρ?v)U′(ρ))dv=0,(25)
V
where the boundary integral vanishes by the same arguments yielding to the vanishing of the boundary integral in (20).Since U(ρ)has a single minimum at v,again the integrand at the left hand side of(25)is non–negative,so the integral vanishes only ifρ=v in all of V,and hence in all of J( .We believe that this result can be extended to more general Abelian models.
IV.CONCLUSIONS
The“no–hair”theorem for purely electric con?gurations of spontaneously broken Abelian models has been extended to general static asymptotically?at black holes.The theorem is gauge invariant,and is established for any model with nonvanishing vacuum expectation values.It is shown that the gauge?eld vanishes outside the black hole.This vanishing is physically due to the e?ective behavior of the gauge?eld as a massive?eld by the spontaneous symmetry breaking.For the particular case of the Abelian Higgs model—Mexican–hat potential—it is additionally shown that the scalar?eld is con?ned to the vacuum in all the black hole exterior,which implies a zero contribution to the right hand side of the Einstein equations(4),and that the only black hole admitted is the Schwarzschild solution.We discuss the main conditions to establish the theorem for purely magnetic con?gurations,but the problem remains still open;we believe that the“no–hair”conjecture applies also to this case.
ACKNOWLEDGMENTS
The author thanks Alberto Garc′?a for useful discussions and very valuable hints,and Thomas Zannias for some considerations,in the early stage of the work,about the correct measure that must be used in the integrals at the horizon.This research was partially supported by the CONACyT Grant32138E and the Sistema Nacional de Investigadores(SNI).The author also thanks all the encouragement and guide provided by his recently late father: Erasmo Ay′o n Alayo.
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超全的英语介词用法归纳总结常用介词基本用法辨析 表示方位的介词：in, to, on 1. in 表示在某地范围之内。 Shanghai is/lies in the east of China. 上海在中国的东部。 2. to 表示在某地范围之外。 Japan is/lies to the east of China. 日本位于中国的东面。 3. on 表示与某地相邻或接壤。 Mongolia is/lies on the north of China. 蒙古国位于中国北边。 表示计量的介词：at, for, by 1. at 表示“以……速度”“以……价格”。 It flies at about 900 kilometers an hour. 它以每小时900公里的速度飞行。 I sold my car at a high price. 我以高价出售了我的汽车。 2. for 表示“用……交换，以……为代价”。 He sold his car for 500 dollars. 他以五百元把车卖了。 注意：at表示单价(price) ，for表示总钱数。
3. by 表示“以……计”，后跟度量单位。 They paid him by the month. 他们按月给他计酬。 Here eggs are sold by weight. 在这里鸡蛋是按重量卖的。 表示材料的介词：of, from, in 1. of 成品仍可看出原料。 This box is made of paper. 这个盒子是纸做的。 2. from 成品已看不出原料。 Wine is made from grapes. 葡萄酒是葡萄酿成的。 3. in 表示用某种材料或语言。 Please fill in the form in pencil first. 请先用铅笔填写这个表格。They talk in English. 他们用英语交谈。 表示工具或手段的介词：by, with, on 1. by 用某种方式，多用于交通。 I went there by bus. 我坐公共汽车去那儿。 2. with表示“用某种工具”。 He broke the window with a stone. 他用石头把玻璃砸坏了。注意：with表示用某种工具时，必须用冠词或物主代词。
for语句可以在命令行提示符中使用，也可以在批处理文件中使用。这两种情况下唯一的区别是%和%%，参加下文说明。 一、for语句的格式： for [参数] 变量in (集合) do 命令[命令的参数] 二、for语句的作用：对集合内的元素逐一执行后面的命令。 1、如：for %%i in (你好) do echo %%i 将在屏幕上显示“你好”2个字。这里集合是“你好”，执行的命令是“echo”。由于集合中只有1个元素，因此循环只运行一次。 如果改成for %%i in (你好朋友) do echo %%i 将会显示2行文字，第一行为“你好”，第二行为“朋友”。因为2个词之间有空格，因此集合中就有了2个元素，循环将运行2次。 2、注意：以上for语句的运行方式是新建一个批处理文件，即扩展名为“.bat”的文件，内容为上面的命令，然后运行。为了批处理执行完不退出，可在最后加上一条pause>null命令，这样能看到执行的结果。要想通过cmd命令行执行的话，必须将%%换成%，即去掉一个%，如下： for %i in (你好) do echo %i 3、以下所有例子都是这样，若要在命令行提示符下执行，请将所有的%%改成一个%。 三、for语句详细说明： 上面语句格式中有的加了中括号[]，表示这个语句元素不是必须的，只在需要时使用。像刚才显示“你好”的命令中就没有使用[参数]这
个语句元素。所有语句元素间用空格隔开。 各语句元素的写法：for、in、do这3个符号是固定不变的 1、[参数]的种类：只有4种，分别是/d、/r、/l、/f（即目录Directory、递归recursion、序列list、文件file），他们用于对后面的集合的含义做出解释，请与下面的集合解释结合来看。这4个参数不区分大小写，可以联合使用，即一条for语句可以出现多个参数。 2、变量：除10个数字外（0－9）的所有符号（因为0－9往往作为形参使用，为了与此区别），变量名一般用单个字母表示即可，而且变量名区分大小写，即A和a是两个不同的变量。变量名前面必须是%，当在命令提示符下执行时，只用一个%；而在批处理程序中，必须用%%。 一行语句中，一般只需定义一个变量。使用/f参数中的tokens 选项可以将集合中的元素分解成多个值，并自动定义新的变量对应这些值。这时语句中可以使用多个变量，通常按字母顺序命名，即第一个是%%a，那么后一个就用%%b。如果第一个是%%i，后一个就用%%j。依此类推。具体看后面的相关内容。 变量可以直接在do后面的命令中使用。每次使用的变量总数不超过52个。 3、集合：集合必须放在括号里。集合是一行文本，这行文本可能有几种类型，如“你好”只是一串字符；“c:\boot.ini”是一个文件；“dir /b”是一个命令。 （1）如果for语句中没有使用任何参数，对待集合文本的处理方式是：
介词for用法归纳 用法1：(表目的)为了。如： They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做？ That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了？ He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的。如： 他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的。如： He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(表利益)为，为了。如： What can I do for you? 你想要我什么？ We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗？ Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者。如： She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意，类似下面这样的句子必须用for： He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思，在一些及物动词后误加介词for： 他们决定在电视上为他们的新产品打广告。 误：They decided to advertise for their new product on TV. 正：They decided to advertise their new product on TV. 注：advertise 可用作及物或不及物动词，但含义不同：advertise sth＝为卖出某物而打广告；advertise for sth＝为寻找某物而打广告。如：advertise for a job=登广告求职。由于受汉语“为”的影响，而此处误加了介词for。类似地，汉语中的“为人民服务”，说成英语是serve the people，而不是serve for the people，“为某人的死报仇”，说成英语是avenge sb’s death，而不是avenge for sb’s death，等等。用法3：(表用途)用于，用来。如： Knives are used for cutting things. 小刀是用来切东西的。 This knife is for cutting bread. 这把小刀是用于切面包的。 It’s a machine for slicing bread. 这是切面包的机器。 The doctor gave her some medicine for her cold. 医生给了她一些感冒药。 用法4：为得到，为拿到，为取得。如： He went home for his book. 他回家拿书。 He went to his friend for advice. 他去向朋友请教。 She often asked her parents for money. 她经常向父母要钱。
【备战高考】英语介词用法总结(完整) 一、单项选择介词 1． passion, people won't have the motivation or the joy necessary for creative thinking. A．For . B．Without C．Beneath D．By 【答案】B 【解析】 【详解】 考查介词辨析。句意：没有激情，人们就不会有创新思维所必须的动机和快乐。A. For 对于；B. Without没有； C. Beneath在……下面 ; D. By通过。没有激情，人们就不会有创新思维所必须的动机和快乐。所以空处填介词without。故填without。 2．Modern zoos should shoulder more social responsibility _______ social progress and awareness of the public. A．in light of B．in favor of C．in honor of D．in praise of 【答案】A 【解析】 【分析】 【详解】 考查介词短语。句意：现代的动物园应该根据社会的进步和公众的意识来承担更多的社会责任。A. in light of根据，鉴于；B. in favor of有利于，支持；C. in honor of 为了纪念；D. in praise of歌颂，为赞扬。此处表示根据，故选A。 3．If we surround ourselves with people _____our major purpose, we can get their support and encouragement. A．in sympathy with B．in terms of C．in honour of D．in contrast with 【答案】A 【解析】 【详解】 考查介词短语辨析。句意：如果我们周围都是认同我们主要前进目标的人，我们就能得到他们的支持和鼓励。A. in sympathy with赞成；B. in terms of 依据；C. in honour of为纪念； D. in contrast with与…形成对比。由“we can get their support and encouragement”可知，in sym pathy with“赞成”符合句意。故选A项。 4．Elizabeth has already achieved success_____her wildest dreams. A．at B．beyond C．within D．upon
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英语介词for的用法归纳总结用法1：(介词for表目的)为了 They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做? That s what we re here for. 这正是我们来的目的。 What s she gone for this time? 她这次去干什么去了? He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的 他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的 He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(介词for表利益)为，为了 What can I do for you? 你想要我什么? We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗?
Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者 She made her daughter a dress. / She made a dress for her daughter. 她为她女儿做了件连衣裙。 He cooked us some potatoes. / He cooked some potatoes for us. 他为我们煮了些土豆。 注意，类似下面这样的句子必须用for： He bought a new chair for the office. 他为办公室买了张新办公椅。 (2) 注意不要按汉语字面意思，在一些及物动词后误加介词for： 他们决定在电视上为他们的新产品打广告。 误：They decided to advertise for their new product on TV. 正：They decided to advertise their new product on TV. 注：advertise 可用作及物或不及物动词，但含义不同：advertise sth=为卖出某物而打广告;advertise for sth=为寻找某物而打广告advertise for a job=登广告求职。由于受汉语为的影响，而此处误加了介词for。类似地，汉语中的为人民服务，说成英语是serve the people，而不是serve for the people，为某人的死报仇，说成英语是avenge sb s death，而不是avenge for sb s death，等等。 用法3：(介词for表用途)用于，用来 Knives are used for cutting things. 小刀是用来切东西的。
批处理命令for语句的基本用法 [系列教程]批处理for语句从入门到精通[20101225更新] ____________________________版主提醒 ____________________________ 文档来自于网络搜索 为了避免影响技术讨论、提高看帖的舒适性，请大家不要在此帖下跟 无实质内容的口水帖，特别是纯顶、纯支持、纯感谢、路过之类的帖子， 管理人员将不定期清理此类回帖，请大家多参与讨论少灌水，与人方便， 终将给自己带来方便，谢谢合作。 ________________________________________________________________ 文档来自于网络搜索 批处理是一门简单的脚本语言，虽然不能独当一面，但是，若作为工作中的辅助工具，绝对会让大家有随用随写、称心如意的畅快感。 文档来自于网络搜索 和其他语言相比，批处理语言有其先天性的优势： 1、系统自带，无需另行安装； 2、命令少，语句简洁，上手非常快； 3、编写出来的脚本小巧玲珑，随写随用； 但是，因为它以命令行方式工作，操作多有不便，在图形界面大行其道的windows世界里，多多少少会让大众望而却步；就算是对命令行有好感的新手，面对微软有如天书的帮助文件，很多人也会败下阵来，因此，论坛里很多会员也发出了编写系统的批处理教程的呼声。
文档来自于网络搜索 编写系统的批处理新手教程，一直是论坛管理层讨论的热点问题，但是，各位管理人员大多都有工作在身，而系统的教程涉及的面是如此之广，面对如此浩大的工程，仅凭一两个人的力量，是难以做好的，因此，本人退而求其次，此次发布的教程，以专题的形式编写，日后人手渐多之后，再考虑组织人力编写全面的教程。 文档来自于网络搜索之所以选择最难的for，一是觉得for最为强大，是大多数人最希望掌握的；二是若写其他命令教程，如果没有for的基础，展开来讲解会无从下手；三是for也是批处理中最复杂最难掌握的语句，把它攻克了，批处理的学习将会一片坦途。 文档来自于网络搜索 这次的for语句系列教程，打算按照for语句的5种句式逐一展开，在讲解for/f的时候，会穿插讲解批处理中一个最为关键、也是新手最容易犯错的概念：变量延迟，大纲如下： 文档来自于网络搜索一前言 二for语句的基本用法 三for /f（含变量延迟） 四for /r 五for /d 六for /l 遵照yibantiaokuan的建议，在顶楼放出此教程的txt版本、word版本和pdf版本，以方便那些离线浏览的会员。 文档来自于网络搜索[本帖最后由namejm于2010-12-26 02:36编辑]
用法1：(表目的)为了。如： They went out for a walk. 他们出去散步了。 What did you do that for? 你干吗这样做? That’s what we’re here for. 这正是我们来的目的。 What’s she gone for this time? 她这次去干什么去了? He was waiting for the bus. 他在等公共汽车。 【用法说明】在通常情况下，英语不用for doing sth 来表示目的。如：他去那儿看他叔叔。 误：He went there for seeing his uncle. 正：He went there to see his uncle. 但是，若一个动名词已名词化，则可与for 连用表目的。如： He went there for swimming. 他去那儿游泳。(swimming 已名词化) 注意：若不是表目的，而是表原因、用途等，则其后可接动名词。(见下面的有关用法) 用法2：(表利益)为，为了。如： What can I do for you? 你想要我什么? We study hard for our motherland. 我们为祖国努力学习。 Would you please carry this for me? 请你替我提这个东西好吗? Do more exercise for the good of your health. 为了健康你要多运动。 【用法说明】(1) 有些后接双宾语的动词(如buy, choose, cook, fetch, find, get, order, prepare, sing, spare 等)，当双宾语易位时，通常用for 来引出间接宾语，表示间接宾语为受益者。如：
批处理命令格式.txt人永远不知道谁哪次不经意的跟你说了再见之后就真的再也不见了。一分钟有多长？这要看你是蹲在厕所里面，还是等在厕所外面……echo 表示显示此命令后的字符 echo off 表示在此语句后所有运行的命令都不显示命令行本身 @与echo off相象，但它是加在每个命令行的最前面，表示运行时不显示这一行的命令行（只能影响当前行）。 call 调用另一个批处理文件（如果不用call而直接调用别的批处理文件，那么执行完那个批处理文件后将无法返回当前文件并执行当前文件的后续命令）。 pause 运行此句会暂停批处理的执行并在屏幕上显示Press any key to continue...的提示，等待用户按任意键后继续 rem 表示此命令后的字符为解释行（注释），不执行，只是给自己今后参考用的（相当于程序中的注释）。 例1：用edit编辑a.bat文件，输入下列内容后存盘为c: a.bat，执行该批处理文件后可实现：将根目录中所有文件写入 a.txt中，启动UCDOS，进入WPS等功能。 批处理文件的内容为: 命令注释： @echo off 不显示后续命令行及当前命令行 dir c: *.* >a.txt 将c盘文件列表写入a.txt call c: ucdos ucdos.bat 调用ucdos echo 你好显示"你好" pause 暂停,等待按键继续 rem 准备运行wps 注释：准备运行wps cd ucdos 进入ucdos目录 wps 运行wps 批处理文件的参数 批处理文件还可以像C语言的函数一样使用参数（相当于DOS命令的命令行参数），这需要用到一个参数表示符“%”。 %[1-9]表示参数，参数是指在运行批处理文件时在文件名后加的以空格（或者Tab）分隔的字符串。变量可以从%0到%9，%0表示批处理命令本身，其它参数字符串用%1到%9顺序表示。例2：C:根目录下有一批处理文件名为f.bat，内容为： @echo off format %1 如果执行C: >f a: 那么在执行f.bat时，%1就表示a:，这样format %1就相当于format a:，于是上面的命令运行时实际执行的是format a: 例3：C:根目录下一批处理文件名为t.bat，内容为: @echo off type %1 type %2 那么运行C: >t a.txt b.txt %1 : 表示a.txt %2 : 表示b.txt 于是上面的命令将顺序地显示a.txt和b.txt文件的内容。 特殊命令 if goto choice for是批处理文件中比较高级的命令，如果这几个你用得很熟练，你就是批
介词for 的常见用法归纳 贵州省黔东南州黎平县黎平一中英语组廖钟雁介词for 用法灵活并且搭配能力很强，是一个使用频率非常高的词，也是 高考必考的重要词汇，现将其常见用法归纳如下，供参考。 1.表时间、距离或数量等。 ①意为“在特定时间，定于，安排在约定时间”。如： The meeting is arranged for 9 o’clock. 会议安排在九点进行。 ②意为“持续达”，常于last、stay 、wait等持续性动词连用，表动作持续的时间，有时可以省略。如： He stayed for a long time. 他逗留了很久。 The meeting lasted （for）three hours. 会议持续了三小时。 ③意为“（距离或数量）计、达”。例如： He walked for two miles. 他走了两英里。 The shop sent me a bill for $100.商店给我送来了100美元的账单。 2. 表方向。意为“向、朝、开往、前往”。常与head、leave 、set off、start 等动词连用。如： Tomorrow Tom will leave for Beijing. 明天汤姆要去北京。 He put on his coat and headed for the door他穿上大衣向门口走去。 介词to也可表示方向，但往往与come、drive 、fly、get、go、lead、march、move、return、ride、travel、walk等动词连用。 3.表示理由或原因,意为“因为、由于”。常与thank、famous、reason 、sake 等词连用。如: Thank you for helping me with my English. 谢谢你帮我学习英语。 For several reasons, I’d rather not meet him. 由于种种原因，我宁可不见他。 The West Lake is famous for its beautiful scenery.西湖因美景而闻名。 4.表示目的,意为“为了、取、买”等。如: Let’s go for a walk. 我们出去散步吧。 I came here for my schoolbag.我来这儿取书包。 He plays the piano for pleasure. 他弹钢琴是为了消遣。 There is no need for anyone to know. 没必要让任何人知道。 5.表示动作的对象或接受者,意为“给、为、对于”。如: Let me pick it up for you. 让我为你捡起来。 Watching TV too much is bad for your health. 看电视太多有害于你的健康。 Here is a letter for you. 这儿有你的一封信。
介词的用法 1.表示地点位置的介词 1)at ,in, on, to，for at (1)表示在小地方; (2)表示“在……附近，旁边” in (1)表示在大地方; (2)表示“在…范围之内”。 on 表示毗邻，接壤，“在……上面”。 to 表示在……范围外，不强调是否接壤；或“到……” 2)above, over, on 在……上 above 指在……上方,不强调是否垂直，与below相对； over指垂直的上方,与under相对,但over与物体有一定的空间，不直接接触。 on表示某物体上面并与之接触。 The bird is flying above my head. There is a bridge over the river. He put his watch on the desk. 3)below, under 在……下面 under表示在…正下方 below表示在……下，不一定在正下方 There is a cat under the table. Please write your name below the line. 4)in front [frant]of, in the front of在……前面 in front of…意思是“在……前面”，指甲物在乙物之前，两者互不包括；其反义词是behind（在……的后面）。There are some flowers in front of the house.(房子前面有些花卉。) in the front of 意思是“在…..的前部”，即甲物在乙物的内部.反义词是at the back of…（在……范围内的后部）。 There is a blackboard in the front of our classroom. 我们的教室前边有一块黑板。 Our teacher stands in the front of the classroom. 我们的老师站在教室前.(老师在教室里) 5）beside，behind beside 表示在……旁边 behind 表示在……后面 2.表示时间的介词 1)in , on，at 在……时 in表示较长时间，如世纪、朝代、时代、年、季节、月及一般（非特指）的早、中、晚等。 如in the 20th century, in the 1950s, in 1989, in summer, in January, in the morning, in one’s life , in one’s thirties等。 on表示具体某一天及其早、中、晚。 如on May 1st, on Monday, on New Year’s Day, on a cold night in January, on a fine morning, on Sunday afternoon等。 at表示某一时刻或较短暂的时间，或泛指圣诞节，复活节等。 如at 3:20, at this time of year, at the beginning of, at the end of …, at the age of …, at Christmas，at night, at noon, at this moment等。 注意：在last, next, this, that, some, every 等词之前一律不用介词。如：We meet every day. 2)in, after 在……之后 “in +段时间”表示将来的一段时间以后； “after+段时间”表示过去的一段时间以后； “after+将来的时间点”表示将来的某一时刻以后。 3)from, since 自从…… from仅说明什么时候开始，不说明某动作或情况持续多久；
批处理文件基础知识 一、单符号message指定让MS-DOS在屏幕上显示的正文 ~ ①在for中表示使用增强的变量扩展。 ②在%var:~n,m%中表示使用扩展环境变量指定位置的字符串。 ③在set/a中表示一元运算符，将操作数按位取反。 ! ①在set /a中一元运算符，表示逻辑非。比如set /a a=!0，这时a就表示逻辑1。 @ ①隐藏命令行本身的回显，常用于批处理中。 % ①在set /a中的二元运算符，表示算术取余。 ②命令行环境下，在for命令in前，后面接一个字符（可以是字母、数字或者一些特定字符），表示指定一个循环或者遍历指标变量。 ③批处理中，后接一个数字表示引用本批处理当前执行时的指定的参数。 ④其它情况下，%将会被脱去（批处理）或保留（命令行） ^ ①取消特定字符的转义作用，比如& | > < ! "等，但不包括%。比如要在屏幕显示一些特殊的字符，比如> >> | ^ &等符号时，就可以在其前面加一个^符号来显示这个^后面的字符了，^^就是显示一个^，^|就是显示一个|字符了; ②在set/a中的二元运算符，表示按位异或。 ③在findstr/r的[]中表示不匹配指定的字符集。 & ①命令连接字符。比如我要在一行文本上同时执行两个命令，就可以用&命令连接这两个命令。 ②在set/a中是按位与。 : ①标签定位符，表示其后的字符串为以标签，可以作为goto命令的作用对象。比如在批处理文件里面定义了一个":begin"标签，用"goto begin"命令就可以转到":begin"标签后面来执行批处理命令了。 ②在%var:string1=string2%中分隔变量名和被替换字串关系。 | ①管道符，就是将上一个命令的输出，作为下一个命令的输入."dir /a/b |more"就可以逐屏的显示dir命令所输出的信息。 ②在set/a中的二元运算符，表示按位或。 ③在帮助文档中表示其前后两个开关、选项或参数是二选一的。 / ①表示其后的字符（串）是命令的功能开关（选项）。比如"dir /s/b/a-d"表示"dir"命令指定的不同的参数。 ②在set/a中表示除法。 > ①命令重定向符，将其前面的命令的输出结果重新定向到其后面的设备中去，后面的设备中的内容被覆盖。比如可以用"dir > lxmxn.txt"将"dir"命令的结果输出到"lxmxn.txt"这个文本文件中去。 ②在findstr/r中表示匹配单词的右边界，需要配合转义字符\使用。 < ①将其后面的文件的内容作为其前面命令的输入。 ②在findstr/r中表示匹配单词的左边界，需要配合转义字符\使用。 . ①在路径的\后紧跟或者单独出现时：
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