relxill_nk: A Relativistic Reflection Model for Testing Einstein’s Gravity
Abstract
:1. Introduction
2. Xray Reflection Spectroscopy
3. The Relativistic Reflection Model relxill_nk
3.1. relxill
 relxill ∼ relconv × xillver.
3.2. Testing the Kerr Black Hole Hypothesis
3.3. relxill_nk
 relxill_nk ∼ relconv_nk × xillver.
4. Observational Constraints
4.1. 1H0707–495
 tbabs × (relxill_nk + diskbb).
 tbabs × (relxill_nk + relxill_nk).
 tbabs × relxill_nk.
4.2. Ark 564
 tbabs × (relxill_nk + xillver).
4.3. GX 339–4
 tbabs × gabs × (relxill_nk + xillver).
4.4. GS 1354–645
 tbabs × relxill_nk.
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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1.  We note that questions remain on the validity of general relativity even at large scales and extremely weak gravitational fields, i.e. the infrared (IR) regime. Tests of general relativity in the IR regime are mainly motivated by the issues of dark matter and dark energy. 
2.  The four free functions f, ${A}_{1}$, ${A}_{2}$, and ${A}_{5}$ are written as a power series in $M/r$
$$\begin{array}{c}f={\sum}_{n=2}^{\infty}{\u03f5}_{n}\frac{{M}^{n}}{{r}^{n2}},\phantom{\rule{2.em}{0ex}}{A}_{1}=1+{\sum}_{n=0}^{\infty}{\alpha}_{1n}{\left(\right)}^{\frac{M}{r}}n,\phantom{\rule{2.em}{0ex}}{A}_{2}=1+{\sum}_{n=0}^{\infty}{\alpha}_{2n}{\left(\right)}^{\frac{M}{r}}n& ,\phantom{\rule{2.em}{0ex}}{A}_{5}=1+{\sum}_{n=0}^{\infty}{\alpha}_{5n}{\left(\right)}^{\frac{M}{r}}n\\ .\end{array}$$

3.  Our current version of relxill_nk is not ready to work with two or more free nonvanishing deformation parameters at the same time. Depending on the specific deformation parameters under consideration, there may be a degeneracy among them, which might be broken in the presence of high quality data or in combination with independent measurements. 
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Bambi, C.; Abdikamalov, A.B.; Ayzenberg, D.; Cao, Z.; Liu, H.; Nampalliwar, S.; Tripathi, A.; WangJi, J.; Xu, Y. relxill_nk: A Relativistic Reflection Model for Testing Einstein’s Gravity. Universe 2018, 4, 79. https://doi.org/10.3390/universe4070079
Bambi C, Abdikamalov AB, Ayzenberg D, Cao Z, Liu H, Nampalliwar S, Tripathi A, WangJi J, Xu Y. relxill_nk: A Relativistic Reflection Model for Testing Einstein’s Gravity. Universe. 2018; 4(7):79. https://doi.org/10.3390/universe4070079
Chicago/Turabian StyleBambi, Cosimo, Askar B. Abdikamalov, Dimitry Ayzenberg, Zheng Cao, Honghui Liu, Sourabh Nampalliwar, Ashutosh Tripathi, Jingyi WangJi, and Yerong Xu. 2018. "relxill_nk: A Relativistic Reflection Model for Testing Einstein’s Gravity" Universe 4, no. 7: 79. https://doi.org/10.3390/universe4070079