Thermodynamics of apparent horizon in brane world scenario
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- 作者：Rong-Gen Cai ; Li-Ming Cao
- 关键词：Cusp anomalous dimension ; Scaling function ; Strong coupling expansion ; Bethe equations ; AdS/CFT correspondence
- 刊名：Nuclear Physics B
- 出版年：2007
- 出版时间：26 November 2007
- 年：2007
- 卷：785
- 期：1-2
- 页码：135-148
- 全文大小：238 K
文摘
In this paper we discuss thermodynamics of apparent horizon of an n-dimensional Friedmann–Robertson–Walker (FRW) universe embedded in an <a name=""mml5"">a><a style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4P2S921-5&_mathId=mml5&_user=10&_cdi=5531&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=eba57de64ad39a8bb6d0a0e7655f0592"" title=""Click to view the MathML source"">(n+1)a>-dimensional AdS space–time. By using the method of unified first law, we give the explicit entropy expression of the apparent horizon of the FRW universe. In the large horizon radius limit, this entropy reduces to the n-dimensional area formula, while in the small horizon radius limit, it obeys the <a name=""mml6"">a><a style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4P2S921-5&_mathId=mml6&_user=10&_cdi=5531&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=6a94a3a633d8155f933aa825ce749ef1"" title=""Click to view the MathML source"">(n+1)a>-dimensional area formula. We also discuss the corresponding bulk geometry and study the apparent horizon extended into the bulk. We calculate the entropy of this apparent horizon by using the area formula of the <a name=""mml7"">a><a style=""text-decoration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4P2S921-5&_mathId=mml7&_user=10&_cdi=5531&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=5bc9ac47f673e2aba7ac84c3f78fc719"" title=""Click to view the MathML source"">(n+1)a>-dimensional bulk. It turns out that both methods give the same result for the apparent horizon entropy. In addition, we show that the Friedmann equation on the brane can be rewritten to a form of the first law, <a name=""mml8"">a><a href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4P2S921-5&_mathId=mml8&_user=10&_cdi=5531&_rdoc=8&_acct=C000050221&_version=1&_userid=10&md5=5dc8044fbf094ec2b4fbb3918180ed04"">![]()
ache/MiamiImageURL/B6TVC-4P2S921-5-1T/0?wchp=dGLbVlb-zSkzV"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=13 width=134>a>, at the apparent horizon.