Logarithmic corrections to thermodynamics of accelerating black holes

As pointed out in recent research, the near extremal black hole entropy with one-loop effect exhibits universal <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>log</a:mi> <a:mi>T</a:mi> </a:math> behavior at sufficiently low temperature. In this paper, we discuss the low-temperature quantum corrections to the thermodynamics of four-dimensional accelerating black holes with rotation and charges by using the method of Euclidean path integral. The one-loop path integral for the black hole thermal partition function near extremality is dominated by zero modes defined with respect to the extremal background. For the accelerating black holes without rotation, the near horizon extremal geometry is a direct product of two dimensional anti-de Sitter space ( <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mrow> <c:msub> <c:mrow> <c:mi>AdS</c:mi> </c:mrow> <c:mrow> <c:mn>2</c:mn> </c:mrow> </c:msub> </c:mrow> </c:math> ) and two sphere ( <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mrow> <e:msup> <e:mrow> <e:mi mathvariant="normal">S</e:mi> </e:mrow> <e:mrow> <e:mn>2</e:mn> </e:mrow> </e:msup> </e:mrow> </e:math> ) with warping factors, and the gravitational zero modes contain both tensor and vector types, with the respective contributions to the near extremal black hole entropy being <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mrow> <h:mo stretchy="false">(</h:mo> <h:mn>3</h:mn> <h:mo>/</h:mo> <h:mn>2</h:mn> <h:mo stretchy="false">)</h:mo> <h:mi>log</h:mi> <h:mi>T</h:mi> </h:mrow> </h:math> and <l:math xmlns:l="http://www.w3.org/1998/Math/MathML" display="inline"> <l:mo stretchy="false">(</l:mo> <l:mn>1</l:mn> <l:mo>/</l:mo> <l:mn>2</l:mn> <l:mo stretchy="false">)</l:mo> <l:mi>log</l:mi> <l:mi>T</l:mi> </l:math> . While in the presence of rotation, the near horizon extremal geometry is a warped and twisted product of <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:msub> <p:mrow> <p:mi>AdS</p:mi> </p:mrow> <p:mrow> <p:mn>2</p:mn> </p:mrow> </p:msub> </p:mrow> </p:math> and <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"> <r:mrow> <r:msup> <r:mrow> <r:mi mathvariant="normal">S</r:mi> </r:mrow> <r:mrow> <r:mn>2</r:mn> </r:mrow> </r:msup> </r:mrow> </r:math> and the gravitational vector modes are absent. For the accelerating black holes with charges, we also consider the one-loop path integral of the gauge field, where the photon zero modes are found to contribute an additional <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mo stretchy="false">(</u:mo> <u:mn>1</u:mn> <u:mo>/</u:mo> <u:mn>2</u:mn> <u:mo stretchy="false">)</u:mo> <u:mi>log</u:mi> <u:mi>T</u:mi> </u:math> term to the near extremal black hole entropy.