Horizon of quantum black holes in various dimensions

详细信息    查看全文

• 作者：Roberto Casadio^a ; ^b ; ^{casadio@bo.infn.it" class="auth_mail" title="E-mail the corresponding author} ; Rogerio T. Cavalcanti^c ; ^{rogerio.cavalcanti@ufabc.edu.br" class="auth_mail" title="E-mail the corresponding author} ; Andrea Giugno^a ; ^b ; ^{andrea.giugno2@unibo.it" class="auth_mail" title="E-mail the corresponding author} ; Jonas Mureika^d ; ^{jmureika@lmu.edu" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Physics Letters B
• 出版年：2016
• 出版时间：10 September 2016
• 年：2016
• 卷：760
• 期：Complete
• 页码：36-44
• 全文大小：481 K

文摘

We adapt the horizon wave-function formalism to describe massive static spherically symmetric sources in a general class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si1.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=24070b7a03107dbb5069b3f97e4e79d7" title="Click to view the MathML source">(1+D)class="mathContainer hidden">class="mathCode">$(1+D)$-dimensional space-time, for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si2.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=aa0c5f109809616484dfbbd9c82706e5" title="Click to view the MathML source">D>3class="mathContainer hidden">class="mathCode">$D>3$ and including the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si3.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=0a0b7645e441558f540b5a314e7288be" title="Click to view the MathML source">D=1class="mathContainer hidden">class="mathCode">$D=1$ case. We find that the probability class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si4.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=23b9a349fefa10ba380daef4af80a67d" title="Click to view the MathML source">P_BHclass="mathContainer hidden">class="mathCode">$P_{\mathrm{BH}}$ that such objects are (quantum) black holes behaves similarly to the probability in the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si5.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=344915ba91b63cf2f5c0bfd154c5d46b" title="Click to view the MathML source">(3+1)class="mathContainer hidden">class="mathCode">$(3+1)$ framework for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si2.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=aa0c5f109809616484dfbbd9c82706e5" title="Click to view the MathML source">D>3class="mathContainer hidden">class="mathCode">$D>3$. In fact, for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si6.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=544d9ba65ea2525d2d4ccfe5adc07e7f" title="Click to view the MathML source">D≥3class="mathContainer hidden">class="mathCode">$D\ge 3$, the probability increases towards unity as the mass grows above the relevant D  -dimensional Planck scale class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si7.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=ce5bf93fdaa6dd94367a24266290a8e7" title="Click to view the MathML source">m_Dclass="mathContainer hidden">class="mathCode">$m_D$. At fixed mass, however, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si4.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=23b9a349fefa10ba380daef4af80a67d" title="Click to view the MathML source">P_BHclass="mathContainer hidden">class="mathCode">$P_{\mathrm{BH}}$ decreases with increasing D  , so that a particle with mass class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si8.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=d112d0e0428cca4223a522603edfd4c9" title="Click to view the MathML source">m≃m_Dclass="mathContainer hidden">class="mathCode">$m\simeq m_D$ has just about class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si9.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=f3b721b3cb2044f4b4c6fee7853fbef5" title="Click to view the MathML source">10%class="mathContainer hidden">class="mathCode">$10\text{\%}$ probability to be a black hole in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si10.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=1c8e80e2fc675475665f46ebca88b635" title="Click to view the MathML source">D=5class="mathContainer hidden">class="mathCode">$D=5$, and smaller for larger D  . This result has a potentially strong impact on estimates of black hole production in colliders. In contrast, for class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si3.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=0a0b7645e441558f540b5a314e7288be" title="Click to view the MathML source">D=1class="mathContainer hidden">class="mathCode">$D=1$, we find the probability is comparably larger for smaller masses, but class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si11.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=9206b393363a61fd259b95233782de71" title="Click to view the MathML source">P_BH<0.5class="mathContainer hidden">class="mathCode">$P_{\mathrm{BH}}<0.5$, suggesting that such lower dimensional black holes are purely quantum and not classical objects. This result is consistent with recent observations that sub-Planckian black holes are governed by an effective two-dimensional gravitation theory. Lastly, we derive Generalised Uncertainty Principle relations for the black holes under consideration, and find a minimum length corresponding to a characteristic energy scale of the order of the fundamental gravitational mass class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si7.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=ce5bf93fdaa6dd94367a24266290a8e7" title="Click to view the MathML source">m_Dclass="mathContainer hidden">class="mathCode">$m_D$ in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si2.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=aa0c5f109809616484dfbbd9c82706e5" title="Click to view the MathML source">D>3class="mathContainer hidden">class="mathCode">$D>3$. For class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0370269316302957&_mathId=si3.gif&_user=111111111&_pii=S0370269316302957&_rdoc=1&_issn=03702693&md5=0a0b7645e441558f540b5a314e7288be" title="Click to view the MathML source">D=1class="mathContainer hidden">class="mathCode">$D=1$ we instead find the uncertainty due to the horizon fluctuations has the same form as the usual Heisenberg contribution, and therefore no fundamental scale exists.