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We construct an effective four-dimensional string-corrected black hole (4D SCBH) by rescaling the string coupling parameter in a D-dimensional Callan–Myers–Perry black hole. From the theoretical point of view, the most interesting findings are that the string corrections coincide with the so-called generalized uncertainty principle (GUP) corrections to black hole solutions, Bekenstein–Hawking entropy acquires logarithmic corrections, and that there exists a critical value of the coupling parameter for which the black hole temperature vanishes. We also find that, due to the string corrections, the nature of the central singularity may be altered from space-like to time-like singularity. In addition, we study the possibility of testing such a black hole with astrophysical observations. Since the dilaton field does not decouple from the metric, it is not a priori clear that the resulting 4D SCBH offers only small corrections to the Schwarzschild black hole. We used motion of the S2 star around the black hole at the center of our galaxy to constrain the parameters (the string coupling parameter and ADM mass) of the 4D SCBH. To test the weak gravity regime, we calculate the deflection angle in this geometry and apply it to gravitational lensing. To test the strong field regime, we calculate the black hole shadow radius. While we find that the observables change as we change the string coupling parameter, the magnitude of the change is too small to distinguish it from the Schwarzschild black hole. With the current precision, to the leading order terms, the 4D SCBH cannot be distinguished from the Schwarzschild black hole.
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A note on a Newtonian approximation in a Schwarzschild background
We consider a (very) simple version of the restricted three body problem in general relativity. The background geometry is given by a Schwarzschild solution governing the motion of two bodies of masses $$m_1$$ and $$m_2$$. We assume that corrections to the trajectory of the body of mass $$m_1$$ due to the presence of the mass $$m_2$$ are given by a Newtonian approximation where Poisson's equation is solved with respect to the Schwarzschild background geometry. Under these assumptions, we derive approximate equations of motion for the corrections to the trajectory of the body of mass $$m_1$$.
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- Award ID(s):
- 1812826
- PAR ID:
- 10105371
- Date Published:
- Journal Name:
- African physical reviews
- Volume:
- 13
- Issue:
- 0
- ISSN:
- 1970-4097
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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