Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry

In the present research note, we discuss the energy–momentum squared gravity model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo>...

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Main Authors: Mohd Danish Siddiqi, Fatemah Mofarreh
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Axioms
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Online Access:https://www.mdpi.com/2075-1680/13/10/708
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author Mohd Danish Siddiqi
Fatemah Mofarreh
author_facet Mohd Danish Siddiqi
Fatemah Mofarreh
author_sort Mohd Danish Siddiqi
collection DOAJ
description In the present research note, we discuss the energy–momentum squared gravity model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-gravity model. Furthermore, we deal with the energy–momentum squared gravity model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">U</mi><mi>n</mi></msub></semantics></math></inline-formula> with hyperbolic Ricci solitons in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-gravity model coupled with perfect fluid and a phantom barrier.
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spelling doaj-art-0477298eec954a019d9bde3978e3ce892025-08-20T02:11:04ZengMDPI AGAxioms2075-16802024-10-01131070810.3390/axioms13100708Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type SymmetryMohd Danish Siddiqi0Fatemah Mofarreh1Department of Mathematics, College of Science, Jazan University, P.O. Box 277, Jazan 45142, Saudi ArabiaMathematical Science Department, Faculty of Science, Princess Nourah bint Abdulrahman University, Riyadh 11546, Saudi ArabiaIn the present research note, we discuss the energy–momentum squared gravity model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> coupled with perfect fluid. We obtain the equation of state for the perfect fluid in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-gravity model. Furthermore, we deal with the energy–momentum squared gravity model <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula> coupled with perfect fluid, which admits the hyperbolic Ricci solitons with a conformal vector field. We provide a clue in this series to determine the density and pressure in the radiation and phantom barrier periods, respectively. Also, we investigate the rate of change in hyperbolic Ricci solitons within the same vector field. In addition, we determine the different energy conditions, black holes and singularity conditions for perfect fluid attached to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-gravity in terms of hyperbolic Ricci solitons. Lastly, we deduce the Schrödinger equation for the potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi mathvariant="script">U</mi><mi>n</mi></msub></semantics></math></inline-formula> with hyperbolic Ricci solitons in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula>-gravity model coupled with perfect fluid and a phantom barrier.https://www.mdpi.com/2075-1680/13/10/708<named-content content-type="equation"><inline-formula> <mml:math id="mm6"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">F</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="script">R</mml:mi> <mml:mo>,</mml:mo> <mml:msup> <mml:mi mathvariant="script">T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-gravityhyperbolic Ricci solitonsperfect fluidconformal vector fieldblack holessingularity
spellingShingle Mohd Danish Siddiqi
Fatemah Mofarreh
Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
Axioms
<named-content content-type="equation"><inline-formula> <mml:math id="mm6"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">F</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="script">R</mml:mi> <mml:mo>,</mml:mo> <mml:msup> <mml:mi mathvariant="script">T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-gravity
hyperbolic Ricci solitons
perfect fluid
conformal vector field
black holes
singularity
title Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
title_full Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
title_fullStr Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
title_full_unstemmed Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
title_short Modified <named-content content-type="equation"><inline-formula><math display="inline"><semantics><mrow><mi mathvariant="script">F</mi><mo>(</mo><mi mathvariant="script">R</mi><mo>,</mo><msup><mi mathvariant="script">T</mi><mn>2</mn></msup><mo>)</mo></mrow></semantics></math></inline-formula></named-content>-Gravity Coupled with Perfect Fluid Admitting Hyperbolic Ricci Soliton Type Symmetry
title_sort modified named content content type equation inline formula math display inline semantics mrow mi mathvariant script f mi mo mo mi mathvariant script r mi mo mo msup mi mathvariant script t mi mn 2 mn msup mo mo mrow semantics math inline formula named content gravity coupled with perfect fluid admitting hyperbolic ricci soliton type symmetry
topic <named-content content-type="equation"><inline-formula> <mml:math id="mm6"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">F</mml:mi> <mml:mo>(</mml:mo> <mml:mi mathvariant="script">R</mml:mi> <mml:mo>,</mml:mo> <mml:msup> <mml:mi mathvariant="script">T</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:semantics> </mml:math> </inline-formula></named-content>-gravity
hyperbolic Ricci solitons
perfect fluid
conformal vector field
black holes
singularity
url https://www.mdpi.com/2075-1680/13/10/708
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