Remarks on Null Geodesics of Born-Infeld Black Holes

<table>The graph shows the closest approach <svg height="11.05" id="M193" style="vertical-align:-3.2316pt" version="1.1" viewbox="0 0 12.1375 11.05" width="12.1375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.05)">
<g transform="translate(72,-63.16)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
</text>
<text transform="matrix(1,0,0,-1,-66.85,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑜</tspan>
</text>
</g>
</g>
</svg> for the effective geometry of the Born-Infeld black hole as a function of the nonlinear parameter <svg height="13.425" id="M194" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 8.8500004 13.425" width="8.8500004" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.425)">
<g transform="translate(72,-61.26)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛽</tspan>
</text>
</g>
</g>
</svg>. Here, <svg height="10.325" id="M195" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 12.7 10.325" width="12.7" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.325)">
<g transform="translate(72,-63.74)">
<text transform="matrix(1,0,0,-1,-71.95,63.79)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐷</tspan>
</text>
</g>
</g>
</svg> is kept fixed at <svg height="11.1" id="M196" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 27.475 11.1" width="27.475" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="9.3772497" y="0">5</tspan>
<tspan style="font-size: 12.50px; " x="15.62875" y="0">6</tspan>
</text>
</g>
</g>
</svg>. Also, <svg height="11.1" id="M197" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 86.012497 11.1" width="86.012497" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,11.1)">
<g transform="translate(72,-63.12)">
<text transform="matrix(1,0,0,-1,-71.95,63.35)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑀</tspan>
<tspan style="font-size: 12.50px; " x="16.028847" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="28.069235" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="34.320736" y="0">.</tspan>
<tspan style="font-size: 12.50px; " x="37.446484" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="43.697987" y="0">6</tspan>
<tspan style="font-size: 12.50px; " x="49.949486" y="0">4</tspan>
<tspan style="font-size: 12.50px; " x="56.200985" y="0">0</tspan>
<tspan style="font-size: 12.50px; " x="62.452484" y="0">5</tspan>
</text>
</g>
</g>
</svg>, <svg height="13.0625" id="M198" style="vertical-align:-1.90608pt" version="1.1" viewbox="0 0 39.537498 13.0625" width="39.537498" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,13.0625)">
<g transform="translate(72,-61.55)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑄</tspan>
<tspan style="font-size: 12.50px; " x="13.228174" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="25.268562" y="0">1</tspan>
</text>
</g>
</g>
</svg>.</table>

International Scholarly Research Notices

Remarks on Null Geodesics of Born-Infeld Black Holes

Figure 9