I think the citations from SN 46.3 and the Milindapañha provided in the other answers are sufficient for answering this question.
However, it think they may not explain the meaning of vitakka & vicara in respect to jhana, let alone in respect to samadhi, because Ajahn Lee Dhammadharo's ideas would imply there is ardency (atappa) in the 1st jhana and no ardency (atappa) in the 2nd, 3rd and 4th jhanas.
However, MN 111 does not distinguish any different supporting mental factors among the different jhanas. Also, MN 19, for example, appears to say a meditator abiding in the 4th jhana has ardency (atappa), however subtle, indirect and/or automatic:
With the giving up of pleasure and pain, and the ending of former
happiness and sadness, I entered and remained in the fourth
absorption, without pleasure or pain, with pure equanimity and
Sukhassa ca pahānā dukkhassa ca pahānā pubbeva somanassadomanassānaṃ
atthaṅgamā adukkhamasukhaṃ upekkhāsatipārisuddhiṃ catutthaṃ jhānaṃ
When my mind had immersed in samādhi like this—purified, bright,
flawless, rid of corruptions, pliable, workable, steady, and
imperturbable — I extended it toward recollection of past nivāsā.
So evaṃ samāhite citte parisuddhe pariyodāte anaṅgaṇe vigatūpakkilese
mudubhūte kammaniye ṭhite āneñjappatte pubbenivāsānussatiñāṇāya cittaṃ
abhininnāmesiṃ. I recollected many kinds of past lives, with features
So anekavihitaṃ pubbenivāsaṃ anussarāmi. Seyyathidaṃ—ekampi jātiṃ … pe
… iti sākāraṃ sauddesaṃ anekavihitaṃ pubbenivāsaṃ anussarāmi.
This was the first knowledge, which I achieved in the first watch of
the night. Ayaṃ kho me, bhikkhave, rattiyā paṭhame yāme paṭhamā vijjā
Ignorance was destroyed and knowledge arose; darkness was destroyed
and light arose, as happens for a meditator who is diligent, keen, and
avijjā vihatā vijjā uppannā; tamo vihato āloko uppanno; yathā taṃ
appamattassa ātāpino pahitattassa viharato.
In my personal experience, vitakka & vicara in respect to samadhi are not as Ajahn Lee Dhammadharo proposed because mindfulness & sampajjana have no direct relationship to vitakka & vicara. Any relationship is merely an indirect consequence that fades in the 2nd jhana.
The function of mindfulness in respect to samadhi development is to maintain sampajjana (situational wisdom), which culminates in keeping the mind free from unwholesome states and making the mind still. Mindfulness establishes a centre point or 'anchor' for the mind.
The result of this mindful stilling of ordinary mental activity is consciousness automatically begins to flow towards or get involved with/land on (upaya; appatiṭṭha; refer to SN 22.53) the in & out breathing.
This automatic non-volitional movement of consciousness towards the breathing is 'vitakka'. The tracking & hugging (anumajjana - lit: 'rubbing') of the breathing by consciousness (which allows the experiencing, feeling & evaluating of the breathing) is 'vicara'.
In the 1st jhana, there remains some subtle movement of consciousness towards (vitakka) and exploration (vicara) of the factors of the 1st jhana, which Ajahn Brahm has described in his book (linked below) as the "Jhana Wobble". However, this vitakka (movement towards) & exploration/ looking around (vicara) cease in the 2nd jhana, where the mind is perfectly still (ekodibhāvaṃ).
Ajahn Buddhadasa said (page 203-204):
Bhikkhu Sujato noted on page 169:
...in some Buddhist works, vitakka and vicāra ‘are apparently looked upon as special faculties in the first jhāna, not as mere thought remaining from ordinary consciousness’.
Ajahn Brahm said on PDF page 30:
Some commentators explain the pair, vitakka and vicára as “initial
thought” and “sustained thought.” While in other contexts this pair
can refer to thought, in jhana they certainly mean something else.