Hawking temperature and the bound on greybody factors in $$D=4$$ double field theory
Abstract
Abstract We investigate the basic properties of Hawking radiation for spherical solutions in $$D=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> double field theory. We give the expression of the Hawking temperature for the solution and then discuss the results of various limits. We find that for all these limits only Schwarzschild solution and F-JNW solution can generate Hawking radiation. Moreover, we obtain the lower bound on greybody factors $$\sigma _l(\omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>l</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> for the spherical solutions in $$D=4$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> double field theory. In particular, we calculate the bound on greybody factors $$\sigma _l(\omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>l</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> for F-JNW solution. For F-JNW solution, $$\sigma _l(\omega )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>σ</mml:mi> <mml:mi>l</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>ω</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> monotonically increases as a and b increase.