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<p>The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3476_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(z-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>axis. It plays an important role in our understanding of the interplay between geometry and matter, and is often used as a proxy for astrophysical environments. Here, we construct the scalar counterpart to the Schwarzschild-Melvin spacetime: a non-asymptotically flat black hole geometry with an everywhere regular scalar field whose gradient is asymptotically aligned with the <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10714_2025_3476_Article_IEq1.gif" Format="GIF" Height="13" Rendition="HTML" Resolution="72" Type="Linedraw" Width="26" /> </InlineMediaObject> <EquationSource Format="TEX">\(z-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>z</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>axis.</p>

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An exact solution describing a scalar counterpart to the Schwarzschild-Melvin Universe

  • 期刊论文

  • 发表日期：

    2025年10月7日

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  • Vitor Cardoso,
  • José Natário

摘要

The Schwarzschild-Melvin spacetime is an exact solution of the Einstein electrovacuum equations describing a black hole immersed in a magnetic field which is asymptotically aligned with the \(z-\) z - axis. It plays an important role in our understanding of the interplay between geometry and matter, and is often used as a proxy for astrophysical environments. Here, we construct the scalar counterpart to the Schwarzschild-Melvin spacetime: a non-asymptotically flat black hole geometry with an everywhere regular scalar field whose gradient is asymptotically aligned with the \(z-\) z - axis.