本文選題：黑洞　切入點(diǎn)：霍金輻射　出處：《大連理工大學(xué)》2010年博士論文

【摘要】： 從上世紀(jì)70年代發(fā)現(xiàn)霍金輻射至今,對(duì)黑洞的研究已經(jīng)取得了長(zhǎng)足的進(jìn)展。雖然尚未確證黑洞的存在,但對(duì)黑洞的理論研究已經(jīng)揭示出一些涉及物理學(xué)和哲學(xué)基本觀念的問(wèn)題,具有劃時(shí)代的意義。 論文首先介紹了霍金輻射出現(xiàn)的的歷史背景及其所帶來(lái)的信息疑難問(wèn)題,即量子純態(tài)演化為熱混合態(tài),違背了量子力學(xué)中的幺正性原理。接著介紹了解決信息疑難問(wèn)題的一種比較好的方法-派瑞克方法。其出發(fā)點(diǎn)是將黑洞的霍金輻射理解成一種量子隧穿,勢(shì)壘強(qiáng)弱取決于出射粒子自身能量的大小。用這種方法,派瑞克等人計(jì)算了零質(zhì)量粒子穿過(guò)Schwarschild黑洞和Reissner-Nordstrom黑洞的出射修正譜。結(jié)果顯示粒子的隧穿幾率和貝根斯坦-霍金熵的變化量有關(guān),出射譜線偏離純熱譜,滿足幺正性原理,支持信息守恒。接下來(lái)把派瑞克方法的推廣到了更一般的穩(wěn)態(tài)黑洞。此外哈密頓-雅克比方法揭示了派瑞克方法的一些不足之處,即用雅克比方法得到的黑洞溫度與霍金得到的并不一致,是后者的兩倍。為了解決這一難題,論文引入了各項(xiàng)同性坐標(biāo)系�？紤]了入射粒子的貢獻(xiàn),得到了正確的霍金溫度,并證明了在派瑞克方法使用的坐標(biāo)系(Painleve-Gullstrand坐標(biāo)系)中入射粒子的貢獻(xiàn)為零。 接下來(lái)介紹了黑洞熵的一些性質(zhì)。根據(jù)黑洞熱力學(xué)第二定律,黑洞熵在數(shù)值上等于黑洞表面積的四分之一,且在順時(shí)方向上永不減少。黑洞外部并不是平靜的,充滿了擾動(dòng)場(chǎng)。一般來(lái)說(shuō),擾動(dòng)場(chǎng)對(duì)黑洞熵的影響表現(xiàn)為黑洞熵公式中增加的一個(gè)對(duì)數(shù)修正項(xiàng)。修正項(xiàng)中的系數(shù)和擾動(dòng)場(chǎng)的模型有關(guān),是待定的。第三章在正則系統(tǒng)中引入拉普拉斯方法計(jì)算了熱場(chǎng)擾動(dòng)對(duì)黑洞熵的修正,因?yàn)檎齽t系統(tǒng)允許黑洞和外界熱場(chǎng)有能量的交換。論文還介紹了另外一套方法,這種方法的主要特點(diǎn)是將黑洞看成一個(gè)處在熱場(chǎng)中的盒子,那么黑洞就會(huì)和它周圍的物質(zhì)達(dá)到熱平衡狀態(tài)。論文將這種方法應(yīng)用到了不同維度的各種黑洞時(shí)空當(dāng)中,得到了一些有用的結(jié)果。最后引入了隨動(dòng)坐標(biāo)系的觀測(cè)者,得出了Schwarzschild黑洞在熱場(chǎng)擾動(dòng)下,隨動(dòng)觀測(cè)者觀測(cè)到的黑洞熵和他所處的位置有關(guān)。 最后,介紹了廣義不確定原理。經(jīng)研究證實(shí),當(dāng)引力效果很弱的時(shí)候,廣義不確定原理可以退化成海森堡不確定關(guān)系；當(dāng)引力場(chǎng)強(qiáng)度不能忽略的時(shí)候,海森堡不確定關(guān)系不能替代廣義不確定原理。根據(jù)廣義不確定原理,位置的不確定度存在一個(gè)最小值。論文用廣義不確定原理研究了量子場(chǎng)擾動(dòng)對(duì)Schwarzschild黑洞熵和溫度的影響。接下來(lái)論文引入了推廣的不確定原理(EUP、GEUP)和修正的不確定原理(MDR),并在各種黑洞時(shí)空中進(jìn)行了推廣,得到了一些比較有用的結(jié)果并進(jìn)行了分析。
[Abstract]:Since the discovery of Hawking radiation in the 1970s, considerable progress has been made in the study of black holes.Although the existence of black hole has not been confirmed, the theoretical study of black hole has revealed some problems related to the basic concepts of physics and philosophy, which is of epoch-making significance.This paper first introduces the historical background of Hawking radiation and the information problems it brings, that is, the evolution of pure quantum states into thermal mixed states, which is contrary to the unitary principle of quantum mechanics.Then it introduces a better method to solve the problem of information-Parrack method.The starting point is to interpret the Hawking radiation of a black hole as a kind of quantum tunneling.Using this method, Parrack et al calculated the emission correction spectra of zero mass particles passing through Schwarschild black holes and Reissner-Nordstrom black holes.The results show that the tunneling probability of particles is related to the change of Baygenstein-Hawking entropy. The emission line deviates from the pure heat spectrum, satisfies the unitary principle, and supports the conservation of information.Then the Parrack method is extended to a more general stationary black hole.In addition, the Hamilton-Jacobian method reveals some shortcomings of the Parrack method, that is, the temperature of the black hole obtained by the Jacobian method is not consistent with that obtained by Hawking, and is twice that of the latter.In order to solve this problem, the same-sex coordinate system is introduced in this paper.Considering the contribution of incident particles, the correct Hawking temperature is obtained, and it is proved that the contribution of incident particles in the Painleve-Gullstrand coordinate system used in the Parrack method is zero.Then some properties of black hole entropy are introduced.According to the second law of black hole thermodynamics, the entropy of the black hole is equal to 1/4 of the surface area of the black hole numerically, and will never decrease in the chronological direction.The outside of the black hole is not calm and full of disturbance fields.Generally speaking, the effect of perturbation field on black hole entropy is expressed as a logarithmic correction term added to the black hole entropy formula.The coefficients in the modified term are dependent on the model of the perturbation field and are to be determined.In the third chapter the Laplace method is introduced into the positive system to calculate the modification of the entropy of the black hole due to the disturbance of the thermal field because the regular system allows the exchange of energy between the black hole and the external thermal field.The paper also introduces another set of methods. The main feature of this method is that the black hole is regarded as a box in the thermal field, then the black hole and the surrounding matter will reach the state of thermal equilibrium.This method is applied to black hole space-time in different dimensions, and some useful results are obtained.Finally, the observators of the following coordinate system are introduced, and the entropy of the Schwarzschild black hole observed by the follower under the disturbance of the thermal field is related to the position of the black hole.Finally, the generalized uncertainty principle is introduced.It is proved that when the gravitational effect is very weak, the generalized uncertainty principle can be degenerated into Heisenberg uncertainty relation, and when the gravitational field intensity cannot be ignored, the Heisenberg uncertainty relation cannot replace the generalized uncertainty principle.According to the generalized uncertainty principle, there exists a minimum value for the uncertainty of position.In this paper, the effect of quantum field perturbation on the entropy and temperature of Schwarzschild black hole is studied by using the generalized uncertainty principle.Then the generalized principle of uncertainty (EUPGE-UPU) and the modified principle of uncertainty (MDR ~ +) are introduced and generalized in various black hole space-time. Some useful results are obtained and analyzed.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2010
【分類號(hào)】：P145.8

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本文編號(hào)：1706163